Research Seminar Algebraic Geometry

New instances of Vojta’s Main Conjecture via Newton-Okounkov bodies and K-(in)stability

Organizer: D. Greb

The goal of the seminar is to understand the relation between Nevanlinna theory and Vojta’s conjecture in Diophantine Geometry on the one side and notions of birational geometry related to linear series and K-stability of Fano varieties on the other side, based on the recent paper arXiv:1901.07942 of Grieve.

Program: has been distributed via eMail; write to to get a copy

Recommendation: For an in-depth introduction to Vojta’s conjecture, the contribution of Vojta to the following volume of lecture notes (which you can download freely if you access it via a UDE-IP-address) is highly recommended: Vojta-survey

No. Date Speaker Title
01 11.04. Daniel Greb Overview and distribution of talks
02 18.04. Anna Piwatz Basics of Nevanlinna Theory
03 25.04. Nils Plewe Cartan’s Theorem
04 02.05. Vytas Paskunas Absolute values and heights on projective spaces
05 09.05. Heer Zhao (Local) Weil functions and height functions with respect to ample divisors
06 16.05. Lukas Pottmeyer Height functions with respect to big divisors, proximity functions,
Vojta’s conjecture and the Arithmetic General Theorem
07 23.05. Tim Kirschner Basics on Okounkov bodies
08 06.06 Daniel Greb / Martin Schwald Concave transforms of Okounkov bodies
09 27.06. Michael Wong K-stability, Kähler-Einstein metrics, and the work of Fujita
10 04.07. Georg Hein Vojta’s conjecture for K-unstable Fanos (following Grieve)
11 11.07. Program discussion for next term